A377521 Antidiagonal sums of A343053.

0, 0, 0, 15, 48, 115, 217, 385, 611, 945, 1366, 1947, 2650, 3575, 4663, 6045, 7637, 9605, 11836, 14535, 17556, 21147, 25125, 29785, 34903, 40825, 47282, 54675, 62686, 71775, 81571, 92597, 104425, 117645, 131768, 147455, 164152, 182595, 202161, 223665, 246411, 271297, 297550

Offset: 0

Author

Stefano Spezia, Jan 03 2025

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).

Crossrefs

Cf. A343053.

Programs

Mathematica

LinearRecurrence[{2,2,-6,0,6,-2,-2,1},{0,0,0,15,48,115,217,385,611,945},43]

Formula

a(n) = (2 - n)*(12*(1 + (-1)^n) - 105*n + 3*(-1)^n*n - 32*n^2 - 4*n^3)/48 for n > 1.

a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8) for n > 9.

G.f.: x^3*(15 + 18*x - 11*x^2 - 19*x^3 + 9*x^4 + 7*x^5 - 3*x^6)/((1 - x)^5*(1 + x)^3).

E.g.f.: (1 - 3*x + 23*x^2/8 + x^3 + x^4/12)*cosh(x) - x*(81 - 72*x - 24*x^2 - 2*x^3)*sinh(x)/24 - 1 + 3*x.